Think - is this number reasonable?

Every so often, numbers get mentioned in the press, on radio or TV, or in conversation, and one wonders if the number is "reasonable".  The late Hans Rosling was very gifted at testing perceptions of numbers relating to health and education.
In England, those of retirement age (roughly those over 65, but this is changing) are entitled to a bus pass which grants free travel on local bus services across the country.  There are restrictions; the pass cannot be used on Monday to Friday before 9:30am to prevent the school and commuter buses being too crowded.  It can't be used on most long-distance services.  But, it is a great boon.  The pass carries an RFID circuit which registers with a sensor on the bus.  
Bus passes of this kind get lost, break or get too close to another RFID sensor which may eliminate the particular signature of the card.
So, someone has to issue replacement cards, and the office for Devon is here in Exeter.  In conversation, I learnt that the workload for the employee charged with the task is "about 15 per day".  Doubtless this employee has other responsibilities, but this is the figure quoted for the number of replacement cards being needed.

Now is 15 a reasonable number for this workload?

Would you expect a number of that size?  Half or less?  Twice it or more?
In the way of all good "Guesstimation" we need some ball-park figures.  The population of Devon is about 900,000 (leaving out Plymouth and Torbay whose local governments have separate arrangements).  Guess one million and you would be reasonably close.  How many are eligible for a bus pass?  Guess less than a quarter, but not much less - let us guess 200,000.  Not all of these will want a bus pass - you need to apply for it - so we might take the council issuing 100,000 passes in all.  15 passes replaced per day implies 100 a week (it wasn't clear if the figure was 15 per working day or 15 per day, so 100 in a week may be too high) and about 5000 per year.  And now the figures do look reasonable.  About 5% of bus passes need to be replaced each year.  And, as further verification of these guesstimates, there is a charge of £10 to replace the pass - so the income is about £50,000 per year, enough to cover a salary and equipment.
Asking if numbers are reasonable is important in O.R. - both for the numbers that are given as input and those which arrive as output from our models.  

O modeller, take care!


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